On the method of Galerkin for the quasilinear parabolic equations in noncylindric domain

This article investigates the boundary value problem for the quasilinear parabolic equations. The existence of solutions in Sobolev's spaces $W_p^{2m,1}$ is proved, as well as the convergent of the approximate solutions, built according to Galerkin's method, to the exact solution with respect to the norm of the space $W_2^{2m,1}$. The estimates of the convergence for some types of nonlinean are obtained.